Trigonometry Review

SIN

H

O

A

θ

TRIGONOMETRY
Finding missing sides of a triangle

TAN

​COS

​COS

LEARNING OUTCOMES

Find missing sides in
right angled triangles

Understand how to

apply SOH-CAH-TOA

Multiple Choice

name the green side

• side

• hypotenuse

• opposite

• adjacent

Multiple Choice

name the red side

• opposite

• hypotenuse

• alternate

• side

Multiple Choice

name the blue side

• opposite

• alternate

• hypotenuse

• side

Multiple Choice

What is the length of the hypotenuse?

• 16
• 30
• 34

Multiple Choice

What is the length of the side opposite ∠X?

• 16
• 30
• 34

Multiple Choice

What is the length of the side adjacent to ∠Z?

• 16
• 30
• 34

TRIGONOMETRY STEPS

1

Identify the opposite,

adjacent and hypotenuse of

the right angled triangle.

Label the Triangle Sides

Use SOH CAH TOA to help
you decide which ratio to

use (sin, cos, tan).

4

Calculate your answer

Complete the calculation

to find your answer. Round
to the required accuracy.

Choose your Ratio
2

3

Applying the formula

Substitute the side

lengths into the correct

formula triangle.

Multiple Choice

what dose SOH stand for

• sin= opposite divided by hypotenuse

• Systematized Organizational Hardware

• sin= opposite minus hypotenuse

• sin= opposite divided by adjacent

Multiple Choice

what dose TOA stand for?

• tan= adjacent divided by opposite

• tan= opposite divided by adjacent

• Transaction Authentication Number

Multiple Choice

What is the saying we use to remember the trig functions?

• SOH CAH TOA

• SAH COH TAO

• COH SAH TOA

• SOH COH TOH

Multiple Choice

$$\sin\theta=$$  

• $$\frac{opposite}{hypotenuse}$$  

• $$\frac{hypotenuse}{opposite}$$  

• $$\frac{adjacent}{hypotenuse}$$  

• $$\frac{opposite}{adjacent}$$  

Multiple Choice

What is the correct ratio?

• 9/41
• 40/41
• 9/40
• 40/9

Multiple Choice

What is the correct ratio?

• 7/24
• 24/7
• 7/25
• 24/25

Multiple Choice

What is the correct ratio?

• 6/10
• 6/8
• 8/10
• 8/6

STEP

1

Label the Triangle Sides

Identify the opposite,
adjacent and hypotenuse
of the right angled triangle.

ONE

Adjacent

x cm

35

15 cm

o

Opposite

Hypotenuse

Decide which side is not
relevant to the
problem: ADJACENT

Choosing the Trigonometric Ratio

The ratio to use (sin, cos, tan)
depends on which side you
know and which side you are
finding. Use SOH CAH TOAto
help you decide.

SOH CAH TOA

STEP TWO

2

Adjacent

x cm

35

15 cm

o

Opposite

Hypotenuse

STEP

3
Applying the formula

Substitute the side lengths
into the correct formula
triangle.

THREE

S

O

H
H =

Sin(35 )

15

o

x cm

35

15 cm

o

Opposite

Hypotenuse

Calculate your answer

Complete the calculation to
find your answer. Round to
the required accuracy.

STEP FOUR

4

H =

Sin(35 )

15

o

H = 26.15

Rounded to 2 d.p.

PRACTICE QUESTIONS

Find the value of x. Give your answers to two decimal places.

1

2

20 cm

32

x cm

o

42

16 cm

o

x cm

PRACTICE QUESTIONS

1

2

20 cm

32

x cm

o

42

16 cm

o

x cm

ANSWERS

16.96 cm
17.77 cm

Math Response

Type answer here

Correct Answer: 14.6

Deg^°

Rad

Math Response

Type answer here

Correct Answer: 17.8

Deg^°

Rad

Math Response

Type answer here

Correct Answer: 38.1

Deg^°

Rad

Math Response

Type answer here

Correct Answer: 27.9

Deg^°

Rad

LEARNING OUTCOMES

Find missing angles in
right angled triangles

Apply trigonometric

rules to solve problems

TRIGONOMETRY STEPS

1

Identify the opposite,

adjacent and hypotenuse of

the right angled triangle.

Label the Triangle Sides

Use SOH CAH TOA to help
you decide which ratio to

use (sin, cos, tan).

4

Calculate your answer

Complete the calculation

to find your answer. Round
to the required accuracy.

Choose your Ratio
2

3

Applying the formula

Substitute the side

lengths into the correct

formula.
Use inverse rule to solve.

1

Adjacent

STEP

Label the Triangle Sides

Identify the opposite,
adjacent and hypotenuse
of the right angled triangle.

ONE

25 cm

15 cm

o

Opposite

Hypotenuse

Decide which side is not
relevant to the
problem: ADJACENT

Choosing the Trigonometric Ratio

The ratio to use (sin, cos, tan)
depends on which side you
know and which side you are
finding. Use SOH CAH TOAto
help you decide.

SOH CAH TOA

STEP TWO

2

Adjacent

25 cm

15 cm

o

Opposite

Hypotenuse

STEP

3 Applying the formula

Substitute the side lengths
into the correct formula
triangle.

THREE

S

O

H

25 cm

15 cm

o

Opposite

Hypotenuse

25

= 15

25

15

o = Sin-1 ( )

​Sin( o)

Calculate your answer

Complete the calculation to
find your answer. Round to
the required accuracy.

STEP FOUR

4

= 36.87

Rounded to 2 d.p.

25

15

o = Sin ( )

-1

o = Sin (0.6)

-1

o

o

Multiple Choice

What is tan 45⁰?

• 1
• 2
• 0.5
• 0.75

Multiple Choice

Solve for x.

• 24.20
• 4.92
• 290.4
• 29.75

Multiple Choice

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle

• 49°
• 57°
• 45°
• 54°

Multiple Choice

Find the missing value.

Round to the nearest tenths.

• 50.6^o

• 29.4^o

• 34.8^o

• 50.1^o

Multiple Choice

Find the measure of the indicated angle (?) round to the nearest tenth.

• 9.4
• 55.2
• 20.15
• 19.4

Multiple Choice

Find the missing value.

Round to the nearest tenths.

• 52.1^o

• 37.9^o

• 52.1 cm

• 50.6 cm

Multiple Choice

Calculate angle DAC.

• 32.11

• 16.92

• 14.25

• 12.07